Celliprismated tesseractic tetracomb

Celliprismated tesseractic tetracomb
Rank	5
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Capotat
Coxeter diagram	x4x3o3o4x ()
Elements
Tera	4N tesseracts, 6N square-octagonal duoprisms, 4N truncated cubic prisms, N truncated tesseracts, N small disprismatotesseractihexadecachora
Cells	16N tetrahedra, 32N triangular prisms, 8N+24N+24N cubes, 24N octagonal prisms, 8N truncated cubes
Faces	64N triangles, 48N+48N+96N squares, 24N octagons
Edges	32N+96N+96N
Vertices	64N
Vertex figure	Triangular antipodial pyramid, edge lengths 1 (small base of antipodium), √2 (sides and other base of antipodium, and lacings to large base), and √2+√2 (lacings to small base)
Related polytopes
Army	Capotat
Regiment	Capotat
Conjugate	Quasicelliquasiprismated tesseractic tetracomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	R5
Convex	Yes

The celliprismated tesseractic tetracomb or capotat, also called the cellitruncated tesseractic tetracomb or steritruncated tesseractic tetracomb is a convex uniform tetracomb. 1 truncated tesseract, 1 small disprismatotesseractihexadecachoron, 1 tesseract, 3 truncated cubic prisms, and 3 square-octagonal duoprisms join at each vertex of this tessellation. As the name suggests, it is the steritruncation of the tesseractic tetracomb.

Vertex coordinates

The vertices of a celliprismated tesseractic tetracomb of edge length 1 are given by all permutations of:

• $\left(±\frac12+(2+\sqrt2)i,\,±\frac{1+\sqrt2}{2}+(2+\sqrt2)j,\,±\frac{1+\sqrt2}{2}+(2+\sqrt2)k,\,±\frac{1+\sqrt2}{2}+(2+\sqrt2)l\right),$

Where i, j, k, and l range over the integers.

External links

• Klitzing, Richard. "capotat".

• Wikipedia Contributors. "Steritruncated tesseractic honeycomb".